### Application of Integrals

goals
The number of solutions for $\cos{x}=x$ is:
Five curves defined as follows
$\displaystyle C_{1}:\left | x+y \right |\leq 1$
$\displaystyle C_{2}:\left | x-y \right |\leq 1$
$\displaystyle C_{3}:\left | x \right |\leq \cfrac{1}{2}$
$\displaystyle C_{4}:\left | y \right |\leq \cfrac{1}{2}$
$\displaystyle C_{5}:3x^{2}+3y^{2}=1$
Draw the asymptotes of $\tan x$ in the interval $\left(0,\dfrac{\pi}{2}\right)$.
The area bounded by the curves $y=\left| x \right| -1$ and $y=-\left| x \right| +1$ is
The area included between the curve ${y}^{2}\left(2a-x\right)={x}^{3}$ is